# Port-Hamiltonian Dynamic Mode Decomposition

arXiv: https://arxiv.org/abs/2204.13474 · HTML: https://mlsanity.com/paper/2204.13474/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Apr 2022.

## Built on by (most cited first, 9 of 9)

- [Pseudo-Hamiltonian Neural Networks with State-Dependent External Forces](https://mlsanity.com/paper/2206.02660/) (2022)
- [Multiplicative Dynamic Mode Decomposition](https://mlsanity.com/paper/2405.05334/) (2024)
- [Nonlinear embeddings for conserving Hamiltonians and other quantities with Neural Galerkin schemes](https://mlsanity.com/paper/2310.07485/) (2023)
- [Data-driven identification of latent port-Hamiltonian systems](https://mlsanity.com/paper/2408.08185/) (2024)
- [Data-driven identification of port-Hamiltonian DAE systems by Gaussian processes](https://mlsanity.com/paper/2406.18726/) (2024)
- [Pseudo-Hamiltonian system identification](https://mlsanity.com/paper/2305.06920/) (2023)
- [Real-Time Motion Detection Using Dynamic Mode Decomposition](https://mlsanity.com/paper/2405.05057/) (2024)
- [On the Generalization of Data-Assisted Control in port-Hamiltonian Systems (DAC-pH)](https://mlsanity.com/paper/2506.07079/) (2025)
- [Deep Embedded Multiplicative DMD for Algebra-Preserving Koopman Learning](https://mlsanity.com/paper/2606.05131/) (2026)

## Abstract (arXiv)

We present a novel physics-informed system identification method to construct a passive linear time-invariant system. In more detail, for a given quadratic energy functional, measurements of the input, state, and output of a system in the time domain, we find a realization that approximates the data well while guaranteeing that the energy functional satisfies a dissipation inequality. To this end, we use the framework of port-Hamiltonian (pH) systems and modify the dynamic mode decomposition, respectively operator inference, to be feasible for continuous-time pH systems. We propose an iterative numerical method to solve the corresponding least-squares minimization problem. We construct an effective initialization of the algorithm by studying the least-squares problem in a weighted norm, for which we present the analytical minimum-norm solution. The efficiency of the proposed method is demonstrated with several numerical examples.